Elliptic curve isogeny class 144.1-g over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-144.1-g
• Conductor: 144.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 144.1-g over \(\Q(\sqrt{22}) \)

Isogeny class 144.1-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
144.1-g1	\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( -14\bigr] \)
144.1-g2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 11032 a + 51745\) , \( 1694014 a + 7945630\bigr] \)
144.1-g3	\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \)
144.1-g4	\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( -16\bigr] \)
144.1-g5	\( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -4\bigr] \)
144.1-g6	\( \bigl[a\) , \( 0\) , \( a\) , \( -97\) , \( -538\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph